Spin excitations used to probe the nature of the exchange coupling in the magnetically ordered ground state of Pr0.5_{0.5}Ca0.5_{0.5}MnO3_{3}

We have used time-of-flight inelastic neutron scattering to measure the spin wave spectrum of the canonical half-doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$, in its magnetic and orbitally ordered phase. The data, which cover multiple Brillouin zones and the entire energy range of the excitations, are compared with several different models that are all consistent with the CE-type magnetic order, but arise through different exchange coupling schemes. The Goodenough model, i.e. an ordered state comprising strong nearest neighbor ferromagnetic interactions along zig-zag chains with antiferromagnetic inter-chain coupling, provides the best description of the data, provided that further neighbor interactions along the chains are included. We are able to rule out a coupling scheme involving formation of strongly bound ferromagnetic dimers, i.e. Zener polarons, on the basis of gross features of the observed spin wave spectrum. A model with weaker dimerization reproduces the observed dispersion but can be ruled out on the basis of discrepancies between the calculated and observed structure factors at certain positions in reciprocal space. Adding further neighbor interactions results in almost no dimerization, i.e. recovery of the Goodenough model. These results are consistent with theoretical analysis of the degenerate double exchange model for half-doping, and provide a recipe for how to interpret future measurements away from half-doping, where degenerate double exchange models predict more complex ground states.Comment: 14 pages, 11 figure

On Pair Content and Variability of Sub-Parsec Jets in Quasars

X-ray observations of blazars associated with the OVV (Optically Violently Variable) quasars put strong constraints on the electron - positron pair content of radio-loud quasar jets. From those observations, we infer that jets in quasars contain many more electron - positron pairs than protons, but dynamically are still dominated by protons. In particular, we show that pure electron - positron jet models can be excluded, as they overpredict soft X-ray radiation; likewise, pure proton - electron jets can be excluded, as they predict too weak nonthermal X-ray radiation. An intermediate case is viable. We demonstrate that jets which are initially proton-electron ("proto-jets") can be pair-loaded via interaction with 100 - 300 keV photons produced in hot accretion disc coronae, likely to exist in active galactic nuclei in general. If the coronal radiation is powered by magnetic flares, the pair loading is expected to be non-uniform and non-axisymmetric. Together with radiation drag, this leads to velocity and density perturbations in a jet and formation of shocks, where the pairs are accelerated. Such a scenario can explain rapid (time scale of about a day) variability observed in OVV quasars.Comment: Accepted for publication in the Astrophysical Journa

Mini Max Wallpaper

Mini Max company formulated a problem for the automatic calculation of the number of wallpaper rolls necessary for decorating a room with wallpaper. The final goal is the development of a web-based calculator open for use to both Mini Max staff and the general public. We propose an approach for reducing the studied problem to the one-dimensional cutting-stock problem. We show this in details for the case of plain wallpapers as well as for the case of patterned wallpapers with straight match. The one-dimensional cutting-stock problem can be formulated as a linear integer programming problem. We develop an approach for calculating the needed number of wallpapers for relatively small problems, create an algorithm in a suitable graphical interface and make different tests. The tests show the efficiency of the proposed approach compared with the existent (available) wallpapers’ calculators

Medical data processing and analysis for remote health and activities monitoring

Recent developments in sensor technology, wearable computing, Internet of Things (IoT), and wireless communication have given rise to research in ubiquitous healthcare and remote monitoring of human\u2019s health and activities. Health monitoring systems involve processing and analysis of data retrieved from smartphones, smart watches, smart bracelets, as well as various sensors and wearable devices. Such systems enable continuous monitoring of patients psychological and health conditions by sensing and transmitting measurements such as heart rate, electrocardiogram, body temperature, respiratory rate, chest sounds, or blood pressure. Pervasive healthcare, as a relevant application domain in this context, aims at revolutionizing the delivery of medical services through a medical assistive environment and facilitates the independent living of patients. In this chapter, we discuss (1) data collection, fusion, ownership and privacy issues; (2) models, technologies and solutions for medical data processing and analysis; (3) big medical data analytics for remote health monitoring; (4) research challenges and opportunities in medical data analytics; (5) examples of case studies and practical solutions

Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

A simple method for finite range decomposition of quadratic forms and Gaussian fields

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagation speed of the wave equation and Chebyshev polynomials. It improves several existing results and also gives simpler proofs.Comment: minor correction for t<